Need Help Understanding Trig Functions

In summary: They came up with the idea of trigonometric functions to represent the ratios of the sides of a triangle.In summary, trigonometric functions are ratios of sides of a triangle and can be easily calculated for simple triangles like 30 and 45 degrees. However, for more complex angles, a calculator is usually used to determine the ratios. The calculator uses methods such as the Cordic method or Taylor series to approximate the values. The concept of trigonometric functions originated from the empirical measurements of different triangles.
  • #1
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All my life I've understood Trig Functions as ratios of sides of a triangles. With this understanding I have been able to get the ratios for simple triangles like 30, 45, etc... since my teachers made me memorize the sides of it...

But now I'd like to know how would you find the ratio of a triangle with an messy angle such as 37 or 98? Most teachers would tell me to punch it in the calculator... but I'd like to have a better understanding than just what my calculator tells me... So I guess what I should be asking is, what does a calculator do to solve the sin/cos/tan of 37,94, 261, etc..? How does it determine what the measurements of a triangle are to get the ratio? I wish to understand trig functions better than just soh/cah/toa and guesstimate.

I only know a little bit of calculus so a simple explanation, if possible, would greatly be appreciated.
 
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  • #2
It's not clear what you are asking. If the "numbers" are messy, the meaning of sine, cosine, etc. is exactly what it is for a 3-4-5 right triangle.

If you are really asking how a calculator does those, check this, about the "Cordic" method:
http://www.dspguru.com/dsp/faqs/cordic
 
  • #3
You could use something like the Taylor series to approximate it, it is a way to approximate functions such as sine as polynomials, the more terms of it you calculate, the more accurate your approximation will be. Obviously, a computer can do a very good approximation very fast.

http://en.wikipedia.org/wiki/Taylor_series
 
  • #4
I've always found the history of trigonometry to be more empirical in the sense that they found their required values by measuring different triangles
 

Related to Need Help Understanding Trig Functions

1. What are the basic trigonometric functions?

The basic trigonometric functions are sine, cosine, and tangent. They represent the ratios of sides of a right triangle and are calculated using the angle of the triangle.

2. How are trigonometric functions used in real life?

Trigonometric functions are used in many fields such as engineering, physics, and navigation. They are used to calculate distances, angles, and heights in real-world situations.

3. What is the unit circle and how does it relate to trigonometric functions?

The unit circle is a circle with a radius of 1 unit. It is used to visualize and understand trigonometric functions. The coordinates of points on the unit circle correspond to the sine and cosine values of the angle formed by the radius and the x-axis.

4. How do I find the values of trigonometric functions for non-right angles?

For non-right angles, you can use a calculator or trigonometric tables to find the values of trigonometric functions. You can also use the unit circle to find the values by using the coordinates of the point on the circle corresponding to the angle.

5. What are the inverse trigonometric functions?

The inverse trigonometric functions are the inverse of the basic trigonometric functions. They are used to find the angle given the ratio of sides of a right triangle. The inverse trigonometric functions are denoted as sin-1, cos-1, and tan-1.

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